The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Este artigo é, em parte, escrito em caráter de revisão e apresenta resultados teóricos recentes sobre problemas de filtragem e previsão linear de processos gaussianos não estacionários. Primeiro, os conceitos básicos, sinal e ruído, são caracterizados matematicamente, e as fontes de informação são definidas por equações diferenciais estocásticas lineares. Em seguida, mostra-se que a solução para um problema convencional de filtragem ou previsão de uma série temporal não estacionária é, em princípio, redutível a um problema, cuja solução é dada pela teoria de Kalman-Bucy, se for possível resolver um problema de encontrar a representação canônica de um processo gaussiano tal que tenha as mesmas funções de covariância que as da série temporal em consideração. No entanto, o problema mencionado acima permanece em aberto. Além disso, o problema da análise tempo-frequência é discutido, e a viabilidade física do analisador evolutivo, isto é, o analisador espectral online, é mostrada. São apresentados métodos para lidar com operadores diferenciais e suas propriedades básicas são esclarecidas. Finalmente, alguns dos problemas abertos relacionados são propostos.
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Tosiro KOGA, "New Vistas to the Signal Processing of Nonstationary Time Series via an Operator Algebraic Way" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 1, pp. 14-30, January 2001, doi: .
Abstract: This paper is, in half part, written in review nature, and presents recent theoretical results on linear-filtering and -prediction problems of nonstationary Gaussian processes. First, the basic concepts, signal and noise, are mathematically characterized, and information sources are defined by linear stochastic differential equations. Then, it is shown that the solution to a conventional problem of filtering or prediction of a nonstationary time series is, in principle, reducible to a problem, of which solution is given by Kalman-Bucy's theory, if one can solve a problem of finding the canonical representation of a Gaussian process such that it has the same covariance functions as those of the time series under consideration. However, the problem mentioned above is left open. Further, the problem of time-frequency analysis is discussed, and physical realizability of the evolutionary, i.e., the online, spectral analyzer is shown. Methods for dealing with differential operators are presented and their basic properties are clarified. Finally, some of related open problems are proposed.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_1_14/_p
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@ARTICLE{e84-a_1_14,
author={Tosiro KOGA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={New Vistas to the Signal Processing of Nonstationary Time Series via an Operator Algebraic Way},
year={2001},
volume={E84-A},
number={1},
pages={14-30},
abstract={This paper is, in half part, written in review nature, and presents recent theoretical results on linear-filtering and -prediction problems of nonstationary Gaussian processes. First, the basic concepts, signal and noise, are mathematically characterized, and information sources are defined by linear stochastic differential equations. Then, it is shown that the solution to a conventional problem of filtering or prediction of a nonstationary time series is, in principle, reducible to a problem, of which solution is given by Kalman-Bucy's theory, if one can solve a problem of finding the canonical representation of a Gaussian process such that it has the same covariance functions as those of the time series under consideration. However, the problem mentioned above is left open. Further, the problem of time-frequency analysis is discussed, and physical realizability of the evolutionary, i.e., the online, spectral analyzer is shown. Methods for dealing with differential operators are presented and their basic properties are clarified. Finally, some of related open problems are proposed.},
keywords={},
doi={},
ISSN={},
month={January},}
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TY - JOUR
TI - New Vistas to the Signal Processing of Nonstationary Time Series via an Operator Algebraic Way
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 14
EP - 30
AU - Tosiro KOGA
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E84-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2001
AB - This paper is, in half part, written in review nature, and presents recent theoretical results on linear-filtering and -prediction problems of nonstationary Gaussian processes. First, the basic concepts, signal and noise, are mathematically characterized, and information sources are defined by linear stochastic differential equations. Then, it is shown that the solution to a conventional problem of filtering or prediction of a nonstationary time series is, in principle, reducible to a problem, of which solution is given by Kalman-Bucy's theory, if one can solve a problem of finding the canonical representation of a Gaussian process such that it has the same covariance functions as those of the time series under consideration. However, the problem mentioned above is left open. Further, the problem of time-frequency analysis is discussed, and physical realizability of the evolutionary, i.e., the online, spectral analyzer is shown. Methods for dealing with differential operators are presented and their basic properties are clarified. Finally, some of related open problems are proposed.
ER -